Seems like you have no idea what mole is
You are calculating number of moles and write that result is a mass. It is not.
the 0.0278g came from 9.73g / 349.0230
moles= mass/molar mass
It is not 9.73g/349.023 - you should list all units. You would get 9.73g/349.023(g/mol) and the result would be 0.0278 mole, not 0.278 g.
Mole is just an overgown dozen - instead of having 12 elements like dozen has, mole has 6.02*10
23 elements.
If there are 0.0278 moles of PbCl
4, how many atoms of Pb? How many atoms of Cl? Knowing how many atoms of Cl in the sample, can you calculate number of moles of chlorine?